Thanks for your reply. It explains why the failure is on glXMakeCurrent. However, I don't believe it's to do with physical video memory. I've tried this out on a number of nvidia cards and the limit is always at the same number.
My colleagues tell me they have experienced a problem like this in the past (at a lower limit of windows) and that a driver upgrade resolved the issue. I did some digging and found that when running the 100.14.19 driver, the limit was 227 windows (almost exactly half of what the current limit is). At the time, my colleagues upgraded to 169.07 (the next driver) and it resolved their problem.
This leads me to believe that the limit is in the driver itself. Is it possible that when upgrading from 100.14.19 to 169.07, a limit in the driver was simply doubled? If so, could it be increased again?